Let us finally note that in the Kähler context, Siu-Yau [1]} showed that if \(X\)  has positive bisectional curvature then \(X\)  is biholomorphic to a complex projective space. Furthermore, a classification of all compact Kähler manifolds with non-negative bisectional curvature was obtained by Mok [2]}, and this can be used along with results of [3]} to give a direct proof of Conjecture REF  in this case.
